Spontaneous emergence of replicators in Artificial Life
Systems Approach

Let's set out to replicate a real time system $S: \mathcal{X} \Rightarrow \mathcal{Y} \; | \; I$, where $\mathcal{X}$ is a empirical continuous history of input and $\mathcal{Y}$ empirical continuous history of output, conditioned upon a real initial system state $I$.  Based on some definition, we require $S$ to be alive.

We cannot simulate a replication of a theoretical model of life, with a selfish gene or any other such attribute, simply because no mathematically terse model on which the simulation could be based exists.  As of this writing, only hints to and minutia of such a model are known.

Furthermore, models are mathematical representations that, throughout human history, are found to be approximations of complexities once anomalies are addressed and new models develop to incorporate them into the theory.1

Simulation Roughly Defined

If we examine a general algorithm $\mathcal{A}$ to replicate $S$, replication can be roughly sketched as follows.


Estimate system $S$, essentially forming hypothesis $H$.
Simulate initial state $I$.
Initiate a series of discrete stimuli $\mathcal{X}_t$ approximating the real and continuous $\mathcal{X}$.
Acquire resulting system behavior $\mathcal{Y}_t$ as discrete observations of $\mathcal{Y}$.
Verify the difference between simulated and actual systems to be within allowable error $\epsilon$. 


Defining Spontaneous Emergence

By spontaneous emergence is meant that such an astronomically large array of initial states and sequences of stimuli occurred that there is a high probability of one of the permutations being alive, based on some specific and reasonable definition of what is living.

Defining What Life Is

Reviewing several definitions of living organisms, the most reasonable definitions include these:


The organism can be distinguished from its environment.
The organism can acquire and cache potential energy and materials required to operate.
Its operation includes continued acquisition, producing a bidirectional and sustainable relationship with its environment.
The organism can roughly reproduce itself.
The reproduction is similar to but not exactly like the parent(s).
The method of energy and materials acquisition may include the consumption of other organisms or its energy and materials.


Competing for resources, natural selection, and all the other features of evolutionary theory are corollary to the above five requirements.  In addition to these, the current trend toward recognizing symbiogenesis as a common theme in the emergence of species should not be dismissed.


Replication of one organism may be influenced by the composition of another organism through forms of assimilation or symbiosis such that traits are passed across categories of organisms.


Artificial Life as a Simulation

These seven criteria poses a challenge for humans attempting to artificially generate life.  It is easy to create a computer model such that life is simulated in some way.  Consider how.


The environment contains virtual energy and virtual matter.
The model of the organism, distinguished from its environment, can acquire its operational requirements from the environment through a set of operations on it.
Mater and energy are conserved because the temperatures are far below nuclear thresholds.
The model of the organism allows acquisition only if enough of the energy and materials acquisition has occurred to maintain the cache.
Mater and energy acquired by one organism cannot be acquired by another organism except by consumption or absorption of an organism that acquired it or produced it from that which was acquired.
The model of the organism can self-replicate in such a way that stochastic differences in the replication is introduced in small quantities.
Operational information, including replication information, may be acquired through consumption or symbiotic relationship under some conditions.


Magical Genes for Spontaneous Life

Notice that the selfish gene is not mentioned above.  Selfishness, the prerequisite of which is intention, is not a requirement for life.  An amoeba does not think selfishly when it moves or eats.  It operates witlessly.  We should not anthropomorphize every organism we study, or develop theory based on anthropomorphic conceptions.

Similarly, symbiotic relationships form that are neither loving nor altruistic.  They exist because there is a mutual benefit that appeared as an unintended byproduct of normal operations and both symbiotic parents happened to pass that symbiotic connection to their respective offspring. 
The mutual benefit, the symbiosis, and the replication are witless and unintended.

There need not be a control mechanism distinct from all other replicated mechanisms to control either symbiotic collaboration or competition.  They too are natural consequences of living things sharing an environment.  Whether an organism dies because it


Lost its symbiont,
Starves because other organisms consumed its necessities,
The organism itself depleted its own resources, or
Those needed resources were otherwise rendered unavailable,


it is still unable to replicate, so its traits die with it.

Note also that there is no known molecule that can replicate itself.  Complex systems of molecules in a variety of chemical states and equilibria are required for reproduction to take place.

Returning to Simulating an Already Existing Organism

Running a time sharing system or distributing these simulated organisms in a parallel processing arrangement may some day simulate a biosphere, but it is not one in that only transistor electro-chemistry is involved.  There is no actual direct relationship between the energy and mater of the system used to assemble the simulation and the energy and mater of the simulated environment in which the simulated systems $S$ reside.

Certainly genetic algorithms, such as Avida and Tierra, have been developed.  Compare those simulations to the modelling scenario described above, and their deficiencies become clear.  Human researchers have not yet found $\mathcal{A}$ to replicate $S$ in a way that aligns with biological reality.

Open-endedness Requires Verification to Have Merit

The most significant limitation on implementations in silico, is that they can never be truly open-ended.

There is no way as of this writing to replicate that which was simulated outside the simulation system.  Until nanotechnology reaches a point where 3D construction and assembly can migrate alive simulations into the unsimulated universe, these simulations are closed-ended in that way and their viability in vito is untested.  The value of open-ended simulations without any way to validate them is essentially zero except for amusement.

Even in the space of digital simulation, as far as that technology has progressed, nothing even close to von Neumann's universal constructor has been accomplished.  Although generic functional copy constructors are available in Scheme, LISP, C++, Java, and later languages, such is a minuscule step toward living objects in computers.

Digital Soup

The simulation of life's origins is considerably more difficult than finding an algorithm $\mathcal{A}$ to replicate $S$, where $S$ is a single life form and a sufficient portion of its environment to be representative of the biosphere on earth with an organism in it.

The issue with primordial digital soup is one of the combinatory explosion.  There are 510 million square Km on the earth's surface, and there are only three categories of life origin time frames possible.


The current estimates are close to correct, that the earth formed 4.54 billion years ago and extremely primitive life emerged 3.5 billion years ago
The organic material found in Canada that is allegedly 3.95 billion years old shortens the gap between planetary formation and life formation on it and older terrestrial life may be found
Vladimir Vernadsky's comment that life may have preexisted earth is more than just a possibility


If we go with the 1.04 billion year gap, then $(4.54 - 3.5) \cdot 10^9 \cdot 510 \cdot 10^6$ Km-years of soup must be simulated, since we cannot assume that life started in the ocean or a puddle or even on the surface.  It could have started underground or in the atmosphere.  The biosphere is currently thought to be 1,800 m above to 8,372 m below thick.

With nanobes being 20 nm in diameter and the possibility that the emergence may have only taken one second we have to simulate in three dimensions over time the following space-time domain in finite elements with at least 50% overlap in all three dimensions.

$$\dfrac {2^3 \cdot (4.54 - 3.5) \cdot 10^9 \cdot 510 \cdot 10^6 \cdot (1,800 - 8,372) \cdot 365.25 \cdot 24 \cdot 60 \cdot 60} {(20 \cdot 10^{-9})^3} \\ = 170,260,472,379 \cdot 10^{9+6+27} = 1.7 \cdot 10^{56}$$

With a quantum computer two stories high the size of Switzerland, the computing time would vastly exceed the duration of the average species on earth.  Humans are likely to be extinct before the computation completes.

As the dating of the oldest found fossils converges on the dating of earth, it may seem that life emerged quickly on earth, but that is not a logical conclusion.  If life formed as soon as the earth cooled sufficiently and no evidence of continuous emergence is found in the remaining billions of years, then Vernadsky's inference that life arrived on earth through one or more of the bodies that struck it becomes more probable.

If that is the case, then one must ask the question, if all assumptions are dropped, whether life had a beginning at all.

Simulating Life Versus Simulating Its Formation

We may simulate what life is, that is, find an algorithm $\mathcal{A}$ to replicate $S$, where $S$ is a single live organism.  It is not realistic to, by brute force, simulate how life began without learning more about what conditions can lead to its formation theoretically to drastically reduce the soup simulation space.  It is that learning that is an ongoing area of research in the genetic algorithm field.

Early musings about the possibility of an algorithm $\mathcal{B}$, which can provide the conditions that allow an arbitrary organism $S$ conforming to the above definition of life to form with out a parent or parents were interesting. Given algorithm $\mathcal{A}$ that simulates a life form and algorithm $\mathcal{B}$ that simulate the formation of life, it may be the later algorithm that proves significantly more difficult.

Conforming physics outside a computer to the simulation may be impossible.  Whether simulated life, when embodied in a robotic system is actually going to be considered life will be left to our descendants, should the species endure sufficiently.

Footnotes

[1] Classic cases include the heliocentric Copernican system giving way to the Law of Gravity, that law being shown an approximation of general relativity as shown by the proper prediction of the orbit of Mercury and light's curvature near the sun, the Four Elements dismissed in light of Lavoisier's discovery of oxygen, and absolute provability of truth within a closed symbolic system disproved by Gödel in his second incompleteness theorem and then recouped partially (in terms of computability) by Turing's completeness theorem.